MAXIMUM K-EQUITABLE LABELING OF GRAPHS

Abstract

In this paper, we define maximum k-equitable labeling of a graph. We prove that the path P_n, star graph K_1,n and bistar graph B_n,n are maximum k-equitable for all n ≥ 2, where n, k ∈ N and k < n. Further, we prove that the cycle C_n is not maximum k-equitable when n ≡ 0 (mod k) and n, k ∈ N. In addition, we show that the cycle C_n is maximum k-equitable when n ≡ r (mod k) where r /= 0, r < k < n and n, r, k ∈ N.